Class 11 Maths - KERALA
Introduction to Three Dimensional Geometry
The chapter Introduction to Three Dimensional Geometry in Class 11 Mathematics for Kerala SCERT students builds upon the two-dimensional coordinate geometry studied earlier. It extends the concepts of coordinates to three-dimensional space by introducing the three mutually perpendicular X, Y, and Z axes, dividing space into eight octants. Students will learn to locate points in 3D space, find the distance between two given points, apply the section formula to divide a line segment in a given ratio, and determine the coordinates of the centroid of a triangle. This chapter serves as a crucial foundation for studying calculus and vectors in higher classes and carries significant weight in board examinations.
Start Learning FreeKey Concepts
Coordinate Axes and Planes
Three mutually perpendicular lines X'OX, Y'OY, and Z'OZ form the coordinate axes, which divide the space into eight parts called octants.
Coordinates of a Point in Space
Any point P in space is represented by an ordered triplet (x, y, z), representing its perpendicular distances from the three coordinate planes.
Distance Formula
The straight-line distance between two points P(x1, y1, z1) and Q(x2, y2, z2) in 3D space is given by the square root of (x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2.
Section Formula
The coordinates of a point dividing the line segment joining two points internally or externally in a given ratio m:n.
Centroid of a Triangle
The point of intersection of the medians of a triangle, whose coordinates are the average of the coordinates of its three vertices.
Important Formulas
Board Exam Info
In the Kerala (SCERT) Class 11 Mathematics examination, this chapter usually carries around 4 to 6 marks. Common question types include finding the distance between two points, proving geometric shapes like triangles or parallelograms using the distance formula, finding coordinates using the section formula, and determining the octant in which a given point lies.
Frequently Asked Questions
How do I know which octant a point lies in?
The sign of the coordinates (x, y, z) determines the octant. For example, if all coordinates are positive (+, +, +), the point lies in the first octant.
Is 3D geometry very different from 2D coordinate geometry?
Not really! The concepts are very similar, but we just add a z-coordinate and a z-axis to account for depth and height in space.
How can I prove that three points are collinear in 3D space?
You can find the distances between the pairs of points (AB, BC, and AC) and show that the sum of the lengths of the two smaller segments equals the longest segment.
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